Multivalued Hardy-Rogers Type ZΘ-Contraction and Generalized Simulation Functions

Ali A., Hussain A., Mitrović Z. D.

Filomat, vol.36, no.1, pp.1-14, 2022 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2201001a
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.1-14
  • Keywords: Data dependence, Hardy-Rogers type contractions, Ulam-Hyres stability, Well-posedness
  • Uşak University Affiliated: No

Abstract

The purpose of this paper is to introduce the notion of multivalued Hardy-Rogers 3Θ-contraction in the sense of generalized simulation functions and to present the corresponding fixed point results with some examples. Moreover, we study the strict fixed point and well-posedness, data dependence, as well as, the Ulam-Hyres stability of the fixed point problem. As an application, we prove the existence of the solution for nonlinear fractional differential equation involving Caputo fractional derivative.